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Abstract

We study the effect of polarization and aperture geometry on the focal spot size of a high numerical aperture (NA) aplanatic lens. We show that for a clear aperture geometry, illuminating the lens by linear or circular polarization is preferable over radial polarization for spot size reduction applications. For annular aperture and objective lenses of 0.85 NA and above we give the sizes of the inner annulus which constitute the transition points to a state where the radial polarization illumination gives smaller spot size. We analyze the evolution, the profile and the effect of transverse and longitudinal field components in the focal plane, and show that they play an opposite role on the spot size in the cases of circular and radial polarization illumination. We show that in the limit of a very thin annulus the radial polarization approaches the prediction of the scalar theory at high NA, whereas the linear and circular polarizations deviate from it. We verify that the longitudinal component generated by radially polarized illumination produces the narrowest spot size for wide range of geometries. Finally, we discuss the effects of tight focusing on a dielectric interface and provide some ideas for circumventing the effects of the interface and even utilize them for spot size reduction.

Fig. 3. Spot size of energy density vs. NA for a clear aperture and radially (triangles) and circularly (circles) input polarized fields. The z component of the radially polarized beam is also shown (rectangles). Inset: zoom in on the high NA section of the graph.

Fig. 4. Spot size of energy density vs. NAmin/NAmax for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams for the case of NAmax of 0.85. The longitudinal component of the radially polarized beam is shown as well (stars).

Fig. 5. Spot size of energy density vs. NAmin/NAmax for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams for the case of NAmax of 0.9. The longitudinal component of the radially polarized beam is shown as well (stars).

Fig. 6. Spot size of energy density vs. NAmin/NAmax for radially (triangles), linearly (circles) and circularly (rectangles) polarized beams for the case of NAmax of 0.95. The longitudinal component of the radially polarized beam is shown as well (stars).

Fig. 11. Spot size of energy density vs. NAmin/NAmax for radially (triangles) and circularly (circles) polarized beams for the case of NAmax of 0.7. The longitudinal component of the radially polarized beam is shown as well (rectangles).

Fig. 12. Cross section of the energy density before and after the interface for the case of passing from a medium with refractive index of 1 a medium with refractive index of 1.5. We use clear aperture illumination with NA of 0.95.

Fig. 14. Cross section of the energy density at the focal plane for the case of passing from refractive index of 1.5 to 3.5 media (red). For comparison, we also plot the energy density for a case focusing through a uniform medium having refractive index of 1 (blue).